# itemfit_bayesian: Bayesian parameter estimation of a test In LatentREGpp: Item Response Theory Implemented in R and Cpp

## Description

Estimates the test parameters according to the Multidimensional Item Response Theory with bayesian adjust for dichotomous data

## Usage

 1 2 3 4 itemfit_bayesian(data, dim, model = "2PL", EMepsilon = 1e-04, clusters = NULL, quad_tech = NULL, quad_points = NULL, individual_weights = as.numeric(c()), initial_values = NULL, noguessing = TRUE, verbose = TRUE, save_time = TRUE) 

## Arguments

 data The matrix containing the answers of tested individuals dim The dimensionality of the test model "1PL", "2PL" or "3PL" EMepsilon Convergence value to determine the accuracy of the test clusters A vector with cluster per dimension quad_tech A string with technique. "Gaussian" for Gaussian quadrature or "QMCEM" for Quasi-Monte Carlo quadrature. If NULL it's selected according to the model's dimension (QMCEM if dim>3). quad_points Amount of quadrature points. If quadratura_technique is "Gaussian". It can be NULL individual_weights A vector with Weights of the quadrature points. initial_values A matrix with initial values for estimation process. Be sure about dimension, model and consistency with data. noguessing In 3PL model and dimension is greater than 1, If true, guessing parameter will not be estimated in zeta vector. Instead c value will have a default initial value. Otherwise guessing parameter will be estimated with zeta vector. verbose True for get information about estimation process in runtime. False in otherwise. save_time True for save estimation time. False otherwise.

## Model

Bayesian model is based in itemfit models. It has a Q_{i} function to optimize according parameters like in itemfit. However this model is given by:

Q_{i} = N * log(P_{ζ_{i}}(ζ_{i})) + \hat{Q_{i}}

Where i index is referenced for items in test.

Then, log posterior is given by:

log(P_{ζ_{i}}(ζ_{i})) = - \frac{N}{2} (\frac{(a_{1i} - μ_{a1i})^2}{σ_{1i}^2} + \cdots + \frac{(a_{Di} - μ_{aDi})^2}{σ_{Di}^2} + \frac{(d_{i} - μ_{di})^2}{σ_{di}^2} + \frac{(c_{i} - μ_{ci})^2}{σ_{ci}^2})

Where a,d and c are parameters, D is the dimension of test. You can give the μ values for each parameters through initial values matrix. In otherwise μ will have default initial values value σ^2 values are constant σ_a^2 = 0.64, σ_d^2 = 4, σ_c^2 = 0.009

LatentREGpp documentation built on April 14, 2017, 11:55 a.m.